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Hybrid fuzzy-stochastic predictive modeling and computation

Banff International Research Station for Mathematical Innovation and Discovery

Predictive computational science is an emerging discipline concerned with assessing the predictability of mathematical and computational tools, particularly in the presence of inevitable uncertainty and limited information. In this talk, I will present a new comprehensive predictive methodology embedded in a new hybrid fuzzy-stochastic framework to predict physical events described by partial differential equations (PDEs) and subject to both random (aleatoric) and non-random (epistemic) uncertainty. In the new framework the uncertain parameters will be characterized by random fields with fuzzy moments. This will result in a new class of PDEs with hybrid fuzzy-stochastic parameters, coined fuzzy-stochastic PDEs, for which forward and inverse problems need to be solved. I will demonstrate the importance and feasibility of the new methodology by applying it to a complex problem: prediction of the response of materials with hierarchical microstructure to external forces. This model problem will serve as an illustrative example, one that cannot be tackled by today’s UQ methodologies.

Mathematics; Probability theory and stochastic processes; Numerical analysis; Industrial mathematics / modelling and simulation

video/mp4

Author affiliation: University of New Mexico

2018-04-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/65175

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/